author | wenzelm |
Fri, 21 Mar 2014 10:45:03 +0100 | |
changeset 56239 | 17df7145a871 |
parent 56002 | 2028467b4df4 |
child 56245 | 84fc7dfa3cd4 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/Datatype/rep_datatype.ML |
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Author: Stefan Berghofer, TU Muenchen |
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Representation of existing types as datatypes: proofs and definitions |
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independent of concrete representation of datatypes (i.e. requiring |
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only abstract properties: injectivity / distinctness of constructors |
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and induction). |
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*) |
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signature REP_DATATYPE = |
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sig |
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val derive_datatype_props : Datatype_Aux.config -> string list -> Datatype_Aux.descr list -> |
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thm -> thm list list -> thm list list -> theory -> string list * theory |
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val rep_datatype : Datatype_Aux.config -> (string list -> Proof.context -> Proof.context) -> |
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term list -> theory -> Proof.state |
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val rep_datatype_cmd : Datatype_Aux.config -> (string list -> Proof.context -> Proof.context) -> |
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string list -> theory -> Proof.state |
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end; |
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structure Rep_Datatype: REP_DATATYPE = |
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struct |
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(** derived definitions and proofs **) |
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(* case distinction theorems *) |
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fun prove_casedist_thms (config : Datatype_Aux.config) |
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new_type_names descr induct case_names_exhausts thy = |
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let |
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val _ = Datatype_Aux.message config "Proving case distinction theorems ..."; |
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val descr' = flat descr; |
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val recTs = Datatype_Aux.get_rec_types descr'; |
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val newTs = take (length (hd descr)) recTs; |
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val maxidx = Thm.maxidx_of induct; |
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val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); |
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fun prove_casedist_thm (i, (T, t)) = |
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let |
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val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) => |
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Abs ("z", T', Const (@{const_name True}, T''))) induct_Ps; |
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val P = |
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Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx + 1), T), Bound 0) $ |
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Var (("P", 0), HOLogic.boolT)); |
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val insts = take i dummyPs @ (P :: drop (i + 1) dummyPs); |
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val cert = cterm_of thy; |
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val insts' = map cert induct_Ps ~~ map cert insts; |
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val induct' = |
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refl RS |
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(nth (Datatype_Aux.split_conj_thm (cterm_instantiate insts' induct)) i RSN (2, rev_mp)); |
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in |
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Goal.prove_sorry_global thy [] |
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(Logic.strip_imp_prems t) |
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(Logic.strip_imp_concl t) |
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(fn {prems, ...} => |
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EVERY |
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[rtac induct' 1, |
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REPEAT (rtac TrueI 1), |
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REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)), |
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REPEAT (rtac TrueI 1)]) |
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end; |
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val casedist_thms = |
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map_index prove_casedist_thm (newTs ~~ Datatype_Prop.make_casedists descr); |
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in |
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thy |
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|> Datatype_Aux.store_thms_atts "exhaust" new_type_names |
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(map single case_names_exhausts) casedist_thms |
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end; |
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(* primrec combinators *) |
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fun prove_primrec_thms (config : Datatype_Aux.config) new_type_names descr |
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injects_of constr_inject (dist_rewrites, other_dist_rewrites) induct thy = |
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let |
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val _ = Datatype_Aux.message config "Constructing primrec combinators ..."; |
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val big_name = space_implode "_" new_type_names; |
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val thy0 = Sign.add_path big_name thy; |
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val descr' = flat descr; |
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val recTs = Datatype_Aux.get_rec_types descr'; |
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val used = fold Term.add_tfree_namesT recTs []; |
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val newTs = take (length (hd descr)) recTs; |
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val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct))); |
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val big_rec_name' = "rec_set_" ^ big_name; |
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val rec_set_names' = |
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if length descr' = 1 then [big_rec_name'] |
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else map (prefix (big_rec_name' ^ "_") o string_of_int) (1 upto length descr'); |
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val rec_set_names = map (Sign.full_bname thy0) rec_set_names'; |
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val (rec_result_Ts, reccomb_fn_Ts) = Datatype_Prop.make_primrec_Ts descr used; |
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val rec_set_Ts = |
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map (fn (T1, T2) => (reccomb_fn_Ts @ [T1, T2]) ---> HOLogic.boolT) (recTs ~~ rec_result_Ts); |
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val rec_fns = |
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map (uncurry (Datatype_Aux.mk_Free "f")) (reccomb_fn_Ts ~~ (1 upto length reccomb_fn_Ts)); |
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val rec_sets' = |
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map (fn c => list_comb (Free c, rec_fns)) (rec_set_names' ~~ rec_set_Ts); |
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val rec_sets = |
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map (fn c => list_comb (Const c, rec_fns)) (rec_set_names ~~ rec_set_Ts); |
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(* introduction rules for graph of primrec function *) |
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fun make_rec_intr T rec_set (cname, cargs) (rec_intr_ts, l) = |
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let |
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fun mk_prem (dt, U) (j, k, prems, t1s, t2s) = |
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let val free1 = Datatype_Aux.mk_Free "x" U j in |
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(case (Datatype_Aux.strip_dtyp dt, strip_type U) of |
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((_, Datatype_Aux.DtRec m), (Us, _)) => |
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let |
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val free2 = Datatype_Aux.mk_Free "y" (Us ---> nth rec_result_Ts m) k; |
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val i = length Us; |
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in |
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(j + 1, k + 1, |
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HOLogic.mk_Trueprop (HOLogic.list_all |
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(map (pair "x") Us, nth rec_sets' m $ |
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Datatype_Aux.app_bnds free1 i $ Datatype_Aux.app_bnds free2 i)) :: prems, |
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free1 :: t1s, free2 :: t2s) |
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end |
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| _ => (j + 1, k, prems, free1 :: t1s, t2s)) |
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end; |
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val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs; |
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val (_, _, prems, t1s, t2s) = fold_rev mk_prem (cargs ~~ Ts) (1, 1, [], [], []); |
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in |
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(rec_intr_ts @ |
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[Logic.list_implies (prems, HOLogic.mk_Trueprop |
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(rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $ |
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list_comb (nth rec_fns l, t1s @ t2s)))], l + 1) |
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end; |
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val (rec_intr_ts, _) = |
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fold (fn ((d, T), set_name) => |
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fold (make_rec_intr T set_name) (#3 (snd d))) (descr' ~~ recTs ~~ rec_sets') ([], 0); |
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|
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val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) = |
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thy0 |
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|> Sign.map_naming Name_Space.conceal |
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|> Inductive.add_inductive_global |
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{quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name', |
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coind = false, no_elim = false, no_ind = true, skip_mono = true} |
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(map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts)) |
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(map dest_Free rec_fns) |
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(map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) [] |
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||> Sign.restore_naming thy0; |
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153 |
|
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(* prove uniqueness and termination of primrec combinators *) |
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155 |
|
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val _ = Datatype_Aux.message config "Proving termination and uniqueness of primrec functions ..."; |
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|
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fun mk_unique_tac ctxt ((((i, (tname, _, constrs)), elim), T), T') (tac, intrs) = |
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let |
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val distinct_tac = |
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if i < length newTs then |
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full_simp_tac (put_simpset HOL_ss ctxt addsimps (nth dist_rewrites i)) 1 |
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else full_simp_tac (put_simpset HOL_ss ctxt addsimps (flat other_dist_rewrites)) 1; |
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164 |
|
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val inject = |
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map (fn r => r RS iffD1) |
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(if i < length newTs then nth constr_inject i else injects_of tname); |
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168 |
|
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fun mk_unique_constr_tac n (cname, cargs) (tac, intr :: intrs, j) = |
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let |
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val k = length (filter Datatype_Aux.is_rec_type cargs); |
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in |
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(EVERY |
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[DETERM tac, |
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REPEAT (etac @{thm ex1E} 1), rtac @{thm ex1I} 1, |
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DEPTH_SOLVE_1 (ares_tac [intr] 1), |
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REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1), |
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etac elim 1, |
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REPEAT_DETERM_N j distinct_tac, |
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TRY (dresolve_tac inject 1), |
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REPEAT (etac conjE 1), hyp_subst_tac ctxt 1, |
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REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]), |
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TRY (hyp_subst_tac ctxt 1), |
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rtac refl 1, |
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REPEAT_DETERM_N (n - j - 1) distinct_tac], |
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intrs, j + 1) |
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end; |
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188 |
|
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val (tac', intrs', _) = |
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fold (mk_unique_constr_tac (length constrs)) constrs (tac, intrs, 0); |
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in (tac', intrs') end; |
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192 |
|
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val rec_unique_thms = |
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let |
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val rec_unique_ts = |
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map (fn (((set_t, T1), T2), i) => |
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Const (@{const_name Ex1}, (T2 --> HOLogic.boolT) --> HOLogic.boolT) $ |
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absfree ("y", T2) (set_t $ Datatype_Aux.mk_Free "x" T1 i $ Free ("y", T2))) |
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(rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs)); |
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val cert = cterm_of thy1; |
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val insts = |
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map (fn ((i, T), t) => absfree ("x" ^ string_of_int i, T) t) |
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((1 upto length recTs) ~~ recTs ~~ rec_unique_ts); |
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val induct' = cterm_instantiate (map cert induct_Ps ~~ map cert insts) induct; |
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205 |
in |
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Datatype_Aux.split_conj_thm (Goal.prove_sorry_global thy1 [] [] |
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(HOLogic.mk_Trueprop (Datatype_Aux.mk_conj rec_unique_ts)) |
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(fn {context = ctxt, ...} => |
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#1 (fold (mk_unique_tac ctxt) (descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts) |
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(((rtac induct' THEN_ALL_NEW Object_Logic.atomize_prems_tac ctxt) 1 THEN |
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rewrite_goals_tac ctxt [mk_meta_eq @{thm choice_eq}], rec_intrs))))) |
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212 |
end; |
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213 |
|
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val rec_total_thms = map (fn r => r RS @{thm theI'}) rec_unique_thms; |
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215 |
|
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(* define primrec combinators *) |
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217 |
|
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val big_reccomb_name = "rec_" ^ space_implode "_" new_type_names; |
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val reccomb_names = |
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map (Sign.full_bname thy1) |
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(if length descr' = 1 then [big_reccomb_name] |
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else map (prefix (big_reccomb_name ^ "_") o string_of_int) (1 upto length descr')); |
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val reccombs = |
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map (fn ((name, T), T') => Const (name, reccomb_fn_Ts @ [T] ---> T')) |
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(reccomb_names ~~ recTs ~~ rec_result_Ts); |
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226 |
|
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val (reccomb_defs, thy2) = |
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thy1 |
56239 | 229 |
|> Sign.add_consts (map (fn ((name, T), T') => |
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(Binding.name (Long_Name.base_name name), reccomb_fn_Ts @ [T] ---> T', NoSyn)) |
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(reccomb_names ~~ recTs ~~ rec_result_Ts)) |
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|> (Global_Theory.add_defs false o map Thm.no_attributes) |
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233 |
(map |
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(fn ((((name, comb), set), T), T') => |
46909 | 235 |
(Binding.name (Thm.def_name (Long_Name.base_name name)), |
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Logic.mk_equals (comb, fold_rev lambda rec_fns (absfree ("x", T) |
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(Const (@{const_name The}, (T' --> HOLogic.boolT) --> T') $ absfree ("y", T') |
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(set $ Free ("x", T) $ Free ("y", T'))))))) |
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(reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) |
52788 | 240 |
||> Sign.parent_path; |
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241 |
|
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242 |
|
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(* prove characteristic equations for primrec combinators *) |
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244 |
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val _ = Datatype_Aux.message config "Proving characteristic theorems for primrec combinators ..."; |
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246 |
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val rec_thms = |
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map (fn t => |
51551 | 249 |
Goal.prove_sorry_global thy2 [] [] t |
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250 |
(fn {context = ctxt, ...} => EVERY |
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[rewrite_goals_tac ctxt reccomb_defs, |
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rtac @{thm the1_equality} 1, |
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resolve_tac rec_unique_thms 1, |
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resolve_tac rec_intrs 1, |
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REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)])) |
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(Datatype_Prop.make_primrecs reccomb_names descr thy2); |
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in |
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thy2 |
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|> Sign.add_path (space_implode "_" new_type_names) |
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|> Global_Theory.note_thmss "" |
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[((Binding.name "rec", [Nitpick_Simps.add]), [(rec_thms, [])])] |
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||> Sign.parent_path |
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|-> (fn thms => pair (reccomb_names, maps #2 thms)) |
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264 |
end; |
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265 |
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266 |
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267 |
(* case combinators *) |
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268 |
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fun prove_case_thms (config : Datatype_Aux.config) |
270 |
new_type_names descr reccomb_names primrec_thms thy = |
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let |
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val _ = Datatype_Aux.message config "Proving characteristic theorems for case combinators ..."; |
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273 |
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val ctxt = Proof_Context.init_global thy; |
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val thy1 = Sign.add_path (space_implode "_" new_type_names) thy; |
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276 |
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val descr' = flat descr; |
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val recTs = Datatype_Aux.get_rec_types descr'; |
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val used = fold Term.add_tfree_namesT recTs []; |
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val newTs = take (length (hd descr)) recTs; |
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val T' = TFree (singleton (Name.variant_list used) "'t", HOLogic.typeS); |
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282 |
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fun mk_dummyT dt = binder_types (Datatype_Aux.typ_of_dtyp descr' dt) ---> T'; |
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284 |
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val case_dummy_fns = |
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map (fn (_, (_, _, constrs)) => map (fn (_, cargs) => |
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let |
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val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs; |
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val Ts' = map mk_dummyT (filter Datatype_Aux.is_rec_type cargs) |
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in Const (@{const_name undefined}, Ts @ Ts' ---> T') end) constrs) descr'; |
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291 |
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val case_names0 = map (fn s => Sign.full_bname thy1 ("case_" ^ s)) new_type_names; |
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293 |
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(* define case combinators via primrec combinators *) |
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295 |
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fun def_case ((((i, (_, _, constrs)), T as Type (Tcon, _)), name), recname) (defs, thy) = |
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if is_some (Ctr_Sugar.ctr_sugar_of ctxt Tcon) then |
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(defs, thy) |
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299 |
else |
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300 |
let |
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301 |
val (fns1, fns2) = split_list (map (fn ((_, cargs), j) => |
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302 |
let |
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val Ts = map (Datatype_Aux.typ_of_dtyp descr') cargs; |
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val Ts' = Ts @ map mk_dummyT (filter Datatype_Aux.is_rec_type cargs); |
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305 |
val frees' = map2 (Datatype_Aux.mk_Free "x") Ts' (1 upto length Ts'); |
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val frees = take (length cargs) frees'; |
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val free = Datatype_Aux.mk_Free "f" (Ts ---> T') j; |
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308 |
in |
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(free, fold_rev (absfree o dest_Free) frees' (list_comb (free, frees))) |
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end) (constrs ~~ (1 upto length constrs))); |
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311 |
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val caseT = map (snd o dest_Free) fns1 @ [T] ---> T'; |
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val fns = flat (take i case_dummy_fns) @ fns2 @ flat (drop (i + 1) case_dummy_fns); |
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val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T'); |
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val decl = ((Binding.name (Long_Name.base_name name), caseT), NoSyn); |
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316 |
val def = |
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(Binding.name (Thm.def_name (Long_Name.base_name name)), |
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Logic.mk_equals (Const (name, caseT), |
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319 |
fold_rev lambda fns1 |
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|
320 |
(list_comb (reccomb, |
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flat (take i case_dummy_fns) @ fns2 @ flat (drop (i + 1) case_dummy_fns))))); |
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322 |
val ([def_thm], thy') = |
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323 |
thy |
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324 |
|> Sign.declare_const_global decl |> snd |
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|> (Global_Theory.add_defs false o map Thm.no_attributes) [def]; |
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in (defs @ [def_thm], thy') end; |
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327 |
|
55402 | 328 |
val (case_defs, thy2) = |
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fold def_case (hd descr ~~ newTs ~~ case_names0 ~~ take (length newTs) reccomb_names) |
55402 | 330 |
([], thy1); |
331 |
||
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332 |
fun prove_case t = |
55402 | 333 |
Goal.prove_sorry_global thy2 [] [] t (fn {context = ctxt, ...} => |
334 |
EVERY [rewrite_goals_tac ctxt (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1]); |
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335 |
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336 |
fun prove_cases (Type (Tcon, _)) ts = |
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(case Ctr_Sugar.ctr_sugar_of ctxt Tcon of |
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338 |
SOME {case_thms, ...} => case_thms |
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| NONE => map prove_case ts); |
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340 |
|
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341 |
val case_thms = |
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map2 prove_cases newTs (Datatype_Prop.make_cases case_names0 descr thy2); |
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343 |
|
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344 |
fun case_name_of (th :: _) = |
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fst (dest_Const (head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of th)))))); |
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346 |
|
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val case_names = map case_name_of case_thms; |
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348 |
in |
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349 |
thy2 |
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|> Context.theory_map ((fold o fold) Nitpick_Simps.add_thm case_thms) |
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351 |
|> Sign.parent_path |
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|> Datatype_Aux.store_thmss "case" new_type_names case_thms |
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353 |
|-> (fn thmss => pair (thmss, case_names)) |
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354 |
end; |
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355 |
|
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356 |
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357 |
(* case splitting *) |
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358 |
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fun prove_split_thms (config : Datatype_Aux.config) |
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360 |
new_type_names case_names descr constr_inject dist_rewrites casedist_thms case_thms thy = |
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361 |
let |
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362 |
val _ = Datatype_Aux.message config "Proving equations for case splitting ..."; |
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363 |
|
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364 |
val descr' = flat descr; |
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365 |
val recTs = Datatype_Aux.get_rec_types descr'; |
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366 |
val newTs = take (length (hd descr)) recTs; |
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367 |
|
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368 |
fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'), exhaustion), case_thms'), T) = |
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369 |
let |
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370 |
val cert = cterm_of thy; |
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371 |
val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion))); |
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val exhaustion' = cterm_instantiate [(cert lhs, cert (Free ("x", T)))] exhaustion; |
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373 |
fun tac ctxt = |
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374 |
EVERY [rtac exhaustion' 1, |
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375 |
ALLGOALS (asm_simp_tac |
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376 |
(put_simpset HOL_ss ctxt addsimps (dist_rewrites' @ inject @ case_thms')))]; |
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377 |
in |
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378 |
(Goal.prove_sorry_global thy [] [] t1 (tac o #context), |
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379 |
Goal.prove_sorry_global thy [] [] t2 (tac o #context)) |
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380 |
end; |
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381 |
|
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382 |
val split_thm_pairs = |
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383 |
map prove_split_thms |
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384 |
(Datatype_Prop.make_splits case_names descr thy ~~ constr_inject ~~ |
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385 |
dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs); |
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|
386 |
|
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387 |
val (split_thms, split_asm_thms) = split_list split_thm_pairs |
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388 |
|
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389 |
in |
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390 |
thy |
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|
391 |
|> Datatype_Aux.store_thms "split" new_type_names split_thms |
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|
392 |
||>> Datatype_Aux.store_thms "split_asm" new_type_names split_asm_thms |
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|
393 |
|-> (fn (thms1, thms2) => pair (thms1 ~~ thms2)) |
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|
394 |
end; |
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changeset
|
395 |
|
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|
396 |
fun prove_weak_case_congs new_type_names case_names descr thy = |
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|
397 |
let |
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changeset
|
398 |
fun prove_weak_case_cong t = |
51551 | 399 |
Goal.prove_sorry_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) |
45907
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changeset
|
400 |
(fn {prems, ...} => EVERY [rtac (hd prems RS arg_cong) 1]); |
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parents:
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changeset
|
401 |
|
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parents:
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changeset
|
402 |
val weak_case_congs = |
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changeset
|
403 |
map prove_weak_case_cong (Datatype_Prop.make_weak_case_congs case_names descr thy); |
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parents:
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changeset
|
404 |
|
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parents:
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changeset
|
405 |
in thy |> Datatype_Aux.store_thms "weak_case_cong" new_type_names weak_case_congs end; |
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changeset
|
406 |
|
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parents:
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changeset
|
407 |
|
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parents:
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changeset
|
408 |
(* additional theorems for TFL *) |
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parents:
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changeset
|
409 |
|
45909 | 410 |
fun prove_nchotomys (config : Datatype_Aux.config) new_type_names descr casedist_thms thy = |
45907
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parents:
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changeset
|
411 |
let |
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parents:
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changeset
|
412 |
val _ = Datatype_Aux.message config "Proving additional theorems for TFL ..."; |
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parents:
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changeset
|
413 |
|
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parents:
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changeset
|
414 |
fun prove_nchotomy (t, exhaustion) = |
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changeset
|
415 |
let |
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changeset
|
416 |
(* For goal i, select the correct disjunct to attack, then prove it *) |
51798 | 417 |
fun tac ctxt i 0 = |
418 |
EVERY [TRY (rtac disjI1 i), hyp_subst_tac ctxt i, REPEAT (rtac exI i), rtac refl i] |
|
419 |
| tac ctxt i n = rtac disjI2 i THEN tac ctxt i (n - 1); |
|
45907
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parents:
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diff
changeset
|
420 |
in |
51551 | 421 |
Goal.prove_sorry_global thy [] [] t |
51798 | 422 |
(fn {context = ctxt, ...} => |
45907
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|
423 |
EVERY [rtac allI 1, |
4b41967bd77e
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changeset
|
424 |
Datatype_Aux.exh_tac (K exhaustion) 1, |
51798 | 425 |
ALLGOALS (fn i => tac ctxt i (i - 1))]) |
45907
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changeset
|
426 |
end; |
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clarified modules that contribute to datatype package;
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parents:
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changeset
|
427 |
|
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changeset
|
428 |
val nchotomys = |
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changeset
|
429 |
map prove_nchotomy (Datatype_Prop.make_nchotomys descr ~~ casedist_thms); |
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parents:
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changeset
|
430 |
|
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parents:
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changeset
|
431 |
in thy |> Datatype_Aux.store_thms "nchotomy" new_type_names nchotomys end; |
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changeset
|
432 |
|
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clarified modules that contribute to datatype package;
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parents:
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changeset
|
433 |
fun prove_case_congs new_type_names case_names descr nchotomys case_thms thy = |
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parents:
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changeset
|
434 |
let |
4b41967bd77e
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parents:
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changeset
|
435 |
fun prove_case_cong ((t, nchotomy), case_rewrites) = |
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parents:
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changeset
|
436 |
let |
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clarified modules that contribute to datatype package;
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parents:
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changeset
|
437 |
val Const ("==>", _) $ tm $ _ = t; |
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parents:
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changeset
|
438 |
val Const (@{const_name Trueprop}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ Ma) = tm; |
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changeset
|
439 |
val cert = cterm_of thy; |
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parents:
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changeset
|
440 |
val nchotomy' = nchotomy RS spec; |
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parents:
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changeset
|
441 |
val [v] = Term.add_vars (concl_of nchotomy') []; |
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changeset
|
442 |
val nchotomy'' = cterm_instantiate [(cert (Var v), cert Ma)] nchotomy'; |
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wenzelm
parents:
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diff
changeset
|
443 |
in |
51551 | 444 |
Goal.prove_sorry_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
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parents:
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changeset
|
445 |
(fn {context = ctxt, prems, ...} => |
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simplifier uses proper Proof.context instead of historic type simpset;
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changeset
|
446 |
let |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
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diff
changeset
|
447 |
val simplify = asm_simp_tac (put_simpset HOL_ss ctxt addsimps (prems @ case_rewrites)) |
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
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diff
changeset
|
448 |
in |
45907
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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diff
changeset
|
449 |
EVERY [ |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
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diff
changeset
|
450 |
simp_tac (put_simpset HOL_ss ctxt addsimps [hd prems]) 1, |
46708
b138dee7bed3
prefer cut_tac, where it is clear that the special variants cut_rules_tac or cut_facts_tac are not required;
wenzelm
parents:
45909
diff
changeset
|
451 |
cut_tac nchotomy'' 1, |
45907
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clarified modules that contribute to datatype package;
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changeset
|
452 |
REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1), |
4b41967bd77e
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changeset
|
453 |
REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)] |
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parents:
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changeset
|
454 |
end) |
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clarified modules that contribute to datatype package;
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parents:
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changeset
|
455 |
end; |
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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changeset
|
456 |
|
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parents:
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changeset
|
457 |
val case_congs = |
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diff
changeset
|
458 |
map prove_case_cong |
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parents:
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diff
changeset
|
459 |
(Datatype_Prop.make_case_congs case_names descr thy ~~ nchotomys ~~ case_thms); |
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parents:
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changeset
|
460 |
|
4b41967bd77e
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parents:
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changeset
|
461 |
in thy |> Datatype_Aux.store_thms "case_cong" new_type_names case_congs end; |
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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changeset
|
462 |
|
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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changeset
|
463 |
|
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clarified modules that contribute to datatype package;
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parents:
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changeset
|
464 |
|
4b41967bd77e
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parents:
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changeset
|
465 |
(** derive datatype props **) |
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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diff
changeset
|
466 |
|
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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diff
changeset
|
467 |
local |
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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diff
changeset
|
468 |
|
45890 | 469 |
fun make_dt_info descr induct inducts rec_names rec_rewrites |
470 |
(index, (((((((((((_, (tname, _, _))), inject), distinct), |
|
471 |
exhaust), nchotomy), case_name), case_rewrites), case_cong), weak_case_cong), |
|
472 |
(split, split_asm))) = |
|
473 |
(tname, |
|
474 |
{index = index, |
|
475 |
descr = descr, |
|
476 |
inject = inject, |
|
477 |
distinct = distinct, |
|
478 |
induct = induct, |
|
479 |
inducts = inducts, |
|
480 |
exhaust = exhaust, |
|
481 |
nchotomy = nchotomy, |
|
482 |
rec_names = rec_names, |
|
483 |
rec_rewrites = rec_rewrites, |
|
484 |
case_name = case_name, |
|
485 |
case_rewrites = case_rewrites, |
|
486 |
case_cong = case_cong, |
|
487 |
weak_case_cong = weak_case_cong, |
|
488 |
split = split, |
|
489 |
split_asm = split_asm}); |
|
490 |
||
45907
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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diff
changeset
|
491 |
in |
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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diff
changeset
|
492 |
|
52788 | 493 |
fun derive_datatype_props config dt_names descr induct inject distinct thy2 = |
45890 | 494 |
let |
495 |
val flat_descr = flat descr; |
|
496 |
val new_type_names = map Long_Name.base_name dt_names; |
|
497 |
val _ = |
|
498 |
Datatype_Aux.message config |
|
499 |
("Deriving properties for datatype(s) " ^ commas_quote new_type_names); |
|
500 |
||
501 |
val (exhaust, thy3) = thy2 |
|
45907
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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diff
changeset
|
502 |
|> prove_casedist_thms config new_type_names descr induct |
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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diff
changeset
|
503 |
(Datatype_Data.mk_case_names_exhausts flat_descr dt_names); |
45890 | 504 |
val (nchotomys, thy4) = thy3 |
45907
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
45901
diff
changeset
|
505 |
|> prove_nchotomys config new_type_names descr exhaust; |
45890 | 506 |
val ((rec_names, rec_rewrites), thy5) = thy4 |
45907
4b41967bd77e
clarified modules that contribute to datatype package;
wenzelm
parents:
45901
diff
changeset
|
507 |
|> prove_primrec_thms config new_type_names descr |
4b41967bd77e
clarified modules that contribute to datatype package;
wenzelm
parents:
45901
diff
changeset
|
508 |
(#inject o the o Symtab.lookup (Datatype_Data.get_all thy4)) inject |
4b41967bd77e
clarified modules that contribute to datatype package;
wenzelm
parents:
45901
diff
changeset
|
509 |
(distinct, Datatype_Data.all_distincts thy2 (Datatype_Aux.get_rec_types flat_descr)) induct; |
45890 | 510 |
val ((case_rewrites, case_names), thy6) = thy5 |
45907
4b41967bd77e
clarified modules that contribute to datatype package;
wenzelm
parents:
45901
diff
changeset
|
511 |
|> prove_case_thms config new_type_names descr rec_names rec_rewrites; |
45890 | 512 |
val (case_congs, thy7) = thy6 |
45907
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clarified modules that contribute to datatype package;
wenzelm
parents:
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diff
changeset
|
513 |
|> prove_case_congs new_type_names case_names descr nchotomys case_rewrites; |
45890 | 514 |
val (weak_case_congs, thy8) = thy7 |
45907
4b41967bd77e
clarified modules that contribute to datatype package;
wenzelm
parents:
45901
diff
changeset
|
515 |
|> prove_weak_case_congs new_type_names case_names descr; |
45890 | 516 |
val (splits, thy9) = thy8 |
45907
4b41967bd77e
clarified modules that contribute to datatype package;
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parents:
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diff
changeset
|
517 |
|> prove_split_thms config new_type_names case_names descr |
4b41967bd77e
clarified modules that contribute to datatype package;
wenzelm
parents:
45901
diff
changeset
|
518 |
inject distinct exhaust case_rewrites; |
45890 | 519 |
|
520 |
val inducts = Project_Rule.projections (Proof_Context.init_global thy2) induct; |
|
521 |
val dt_infos = |
|
522 |
map_index |
|
523 |
(make_dt_info flat_descr induct inducts rec_names rec_rewrites) |
|
524 |
(hd descr ~~ inject ~~ distinct ~~ exhaust ~~ nchotomys ~~ |
|
525 |
case_names ~~ case_rewrites ~~ case_congs ~~ weak_case_congs ~~ splits); |
|
526 |
val dt_names = map fst dt_infos; |
|
527 |
val prfx = Binding.qualify true (space_implode "_" new_type_names); |
|
528 |
val simps = flat (inject @ distinct @ case_rewrites) @ rec_rewrites; |
|
45901
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
529 |
val named_rules = flat (map_index (fn (i, tname) => |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
530 |
[((Binding.empty, [Induct.induct_type tname]), [([nth inducts i], [])]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
531 |
((Binding.empty, [Induct.cases_type tname]), [([nth exhaust i], [])])]) dt_names); |
45890 | 532 |
val unnamed_rules = map (fn induct => |
45901
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
533 |
((Binding.empty, [Rule_Cases.inner_rule, Induct.induct_type ""]), [([induct], [])])) |
45890 | 534 |
(drop (length dt_names) inducts); |
51673
4dfa00e264d8
separate data used for case translation from the datatype package
traytel
parents:
51672
diff
changeset
|
535 |
|
4dfa00e264d8
separate data used for case translation from the datatype package
traytel
parents:
51672
diff
changeset
|
536 |
val ctxt = Proof_Context.init_global thy9; |
55954 | 537 |
val case_combs = |
56002 | 538 |
map (Proof_Context.read_const {proper = true, strict = true} ctxt) case_names; |
51673
4dfa00e264d8
separate data used for case translation from the datatype package
traytel
parents:
51672
diff
changeset
|
539 |
val constrss = map (fn (dtname, {descr, index, ...}) => |
56002 | 540 |
map (Proof_Context.read_const {proper = true, strict = true} ctxt o fst) |
55954 | 541 |
(#3 (the (AList.lookup op = descr index)))) dt_infos; |
45890 | 542 |
in |
543 |
thy9 |
|
45901
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
544 |
|> Global_Theory.note_thmss "" |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
545 |
([((prfx (Binding.name "simps"), []), [(simps, [])]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
546 |
((prfx (Binding.name "inducts"), []), [(inducts, [])]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
547 |
((prfx (Binding.name "splits"), []), [(maps (fn (x, y) => [x, y]) splits, [])]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
548 |
((Binding.empty, [Simplifier.simp_add]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
549 |
[(flat case_rewrites @ flat distinct @ rec_rewrites, [])]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
550 |
((Binding.empty, [Code.add_default_eqn_attribute]), [(rec_rewrites, [])]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
551 |
((Binding.empty, [iff_add]), [(flat inject, [])]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
552 |
((Binding.empty, [Classical.safe_elim NONE]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
553 |
[(map (fn th => th RS notE) (flat distinct), [])]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
554 |
((Binding.empty, [Simplifier.cong_add]), [(weak_case_congs, [])]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
555 |
((Binding.empty, [Induct.induct_simp_add]), [(flat (distinct @ inject), [])])] @ |
45890 | 556 |
named_rules @ unnamed_rules) |
557 |
|> snd |
|
558 |
|> Datatype_Data.register dt_infos |
|
51673
4dfa00e264d8
separate data used for case translation from the datatype package
traytel
parents:
51672
diff
changeset
|
559 |
|> Context.theory_map (fold2 Case_Translation.register case_combs constrss) |
45890 | 560 |
|> Datatype_Data.interpretation_data (config, dt_names) |
561 |
|> pair dt_names |
|
562 |
end; |
|
563 |
||
45907
4b41967bd77e
clarified modules that contribute to datatype package;
wenzelm
parents:
45901
diff
changeset
|
564 |
end; |
4b41967bd77e
clarified modules that contribute to datatype package;
wenzelm
parents:
45901
diff
changeset
|
565 |
|
45890 | 566 |
|
567 |
||
568 |
(** declare existing type as datatype **) |
|
569 |
||
570 |
local |
|
571 |
||
572 |
fun prove_rep_datatype config dt_names descr raw_inject half_distinct raw_induct thy1 = |
|
573 |
let |
|
574 |
val raw_distinct = (map o maps) (fn thm => [thm, thm RS not_sym]) half_distinct; |
|
575 |
val new_type_names = map Long_Name.base_name dt_names; |
|
576 |
val prfx = Binding.qualify true (space_implode "_" new_type_names); |
|
45901
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
577 |
val (((inject, distinct), [(_, [induct])]), thy2) = |
45890 | 578 |
thy1 |
579 |
|> Datatype_Aux.store_thmss "inject" new_type_names raw_inject |
|
580 |
||>> Datatype_Aux.store_thmss "distinct" new_type_names raw_distinct |
|
45901
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
581 |
||>> Global_Theory.note_thmss "" |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
582 |
[((prfx (Binding.name "induct"), [Datatype_Data.mk_case_names_induct descr]), |
cea7cd0c7e99
eliminated old-fashioned Global_Theory.add_thms(s);
wenzelm
parents:
45891
diff
changeset
|
583 |
[([raw_induct], [])])]; |
45890 | 584 |
in |
585 |
thy2 |
|
586 |
|> derive_datatype_props config dt_names [descr] induct inject distinct |
|
587 |
end; |
|
588 |
||
589 |
fun gen_rep_datatype prep_term config after_qed raw_ts thy = |
|
590 |
let |
|
591 |
val ctxt = Proof_Context.init_global thy; |
|
592 |
||
593 |
fun constr_of_term (Const (c, T)) = (c, T) |
|
594 |
| constr_of_term t = error ("Not a constant: " ^ Syntax.string_of_term ctxt t); |
|
595 |
fun no_constr (c, T) = |
|
55304 | 596 |
error ("Bad constructor: " ^ Proof_Context.markup_const ctxt c ^ "::" ^ |
45890 | 597 |
Syntax.string_of_typ ctxt T); |
598 |
fun type_of_constr (cT as (_, T)) = |
|
599 |
let |
|
600 |
val frees = Term.add_tfreesT T []; |
|
601 |
val (tyco, vs) = (apsnd o map) dest_TFree (dest_Type (body_type T)) |
|
602 |
handle TYPE _ => no_constr cT |
|
603 |
val _ = if has_duplicates (eq_fst (op =)) vs then no_constr cT else (); |
|
604 |
val _ = if length frees <> length vs then no_constr cT else (); |
|
605 |
in (tyco, (vs, cT)) end; |
|
606 |
||
607 |
val raw_cs = |
|
608 |
AList.group (op =) (map (type_of_constr o constr_of_term o prep_term thy) raw_ts); |
|
609 |
val _ = |
|
610 |
(case map_filter (fn (tyco, _) => |
|
611 |
if Symtab.defined (Datatype_Data.get_all thy) tyco then SOME tyco else NONE) raw_cs of |
|
612 |
[] => () |
|
49020
f379cf5d71bd
more work on BNF sugar -- up to derivation of nchotomy
blanchet
parents:
46961
diff
changeset
|
613 |
| tycos => error ("Type(s) " ^ commas_quote tycos ^ " already represented inductively")); |
45890 | 614 |
val raw_vss = maps (map (map snd o fst) o snd) raw_cs; |
615 |
val ms = |
|
616 |
(case distinct (op =) (map length raw_vss) of |
|
617 |
[n] => 0 upto n - 1 |
|
618 |
| _ => error "Different types in given constructors"); |
|
619 |
fun inter_sort m = |
|
620 |
map (fn xs => nth xs m) raw_vss |
|
621 |
|> foldr1 (Sorts.inter_sort (Sign.classes_of thy)); |
|
622 |
val sorts = map inter_sort ms; |
|
623 |
val vs = Name.invent_names Name.context Name.aT sorts; |
|
624 |
||
625 |
fun norm_constr (raw_vs, (c, T)) = |
|
626 |
(c, map_atyps |
|
627 |
(TFree o (the o AList.lookup (op =) (map fst raw_vs ~~ vs)) o fst o dest_TFree) T); |
|
628 |
||
629 |
val cs = map (apsnd (map norm_constr)) raw_cs; |
|
630 |
val dtyps_of_typ = map (Datatype_Aux.dtyp_of_typ (map (rpair vs o fst) cs)) o binder_types; |
|
631 |
val dt_names = map fst cs; |
|
632 |
||
633 |
fun mk_spec (i, (tyco, constr)) = |
|
634 |
(i, (tyco, map Datatype_Aux.DtTFree vs, (map o apsnd) dtyps_of_typ constr)); |
|
635 |
val descr = map_index mk_spec cs; |
|
636 |
val injs = Datatype_Prop.make_injs [descr]; |
|
637 |
val half_distincts = Datatype_Prop.make_distincts [descr]; |
|
638 |
val ind = Datatype_Prop.make_ind [descr]; |
|
639 |
val rules = (map o map o map) Logic.close_form [[[ind]], injs, half_distincts]; |
|
640 |
||
641 |
fun after_qed' raw_thms = |
|
642 |
let |
|
643 |
val [[[raw_induct]], raw_inject, half_distinct] = |
|
644 |
unflat rules (map Drule.zero_var_indexes_list raw_thms); |
|
645 |
(*FIXME somehow dubious*) |
|
646 |
in |
|
647 |
Proof_Context.background_theory_result (* FIXME !? *) |
|
648 |
(prove_rep_datatype config dt_names descr raw_inject half_distinct raw_induct) |
|
649 |
#-> after_qed |
|
650 |
end; |
|
651 |
in |
|
652 |
ctxt |
|
653 |
|> Proof.theorem NONE after_qed' ((map o map) (rpair []) (flat rules)) |
|
654 |
end; |
|
655 |
||
656 |
in |
|
657 |
||
658 |
val rep_datatype = gen_rep_datatype Sign.cert_term; |
|
659 |
val rep_datatype_cmd = gen_rep_datatype Syntax.read_term_global; |
|
660 |
||
661 |
end; |
|
662 |
||
663 |
||
664 |
(* outer syntax *) |
|
665 |
||
666 |
val _ = |
|
46961
5c6955f487e5
outer syntax command definitions based on formal command_spec derived from theory header declarations;
wenzelm
parents:
46909
diff
changeset
|
667 |
Outer_Syntax.command @{command_spec "rep_datatype"} "represent existing types inductively" |
45890 | 668 |
(Scan.repeat1 Parse.term >> (fn ts => |
669 |
Toplevel.print o |
|
670 |
Toplevel.theory_to_proof (rep_datatype_cmd Datatype_Aux.default_config (K I) ts))); |
|
671 |
||
672 |
end; |